Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Equivalent Representations: Rational Functions, Exercise 21: Exercise 4D

Sketch the graph of the function $y=\frac{5}{3x-6}+2$. Show the asymptotes as dotted lines and state the domain and range. 

Sketch the graph of the function $y=\frac{1}{2-x}+1$. Show the asymptotes as dotted lines and state the domain and range. 

When lightning strikes, you see the flash almost instantly, but the sound of the thunder reaches you later, as sound travels at approximately $330 \mathrm{m}{ \mathrm{s}}^{-1}$. The speed of the sound is affected by temperature of the surrounding air. The time sound takes to travel one kilometre is modelled by $t=\frac{1000}{0.6c+330}$, where $t$ is the time in seconds and $c$ is the air temperature in Celsius. Sketch the graph of $t$ for $-20\le c\le 40$ where $c$ is the temperature in ${}^{\circ }\mathrm{C}$. 

When lightning strikes, you see the flash almost instantly, but the sound of the thunder reaches you later, as sound travels at approximately $330 \mathrm{m}{ \mathrm{s}}^{-1}$. The speed of the sound is affected by temperature of the surrounding air. The time sound takes to travel one kilometre is modelled by $t=\frac{1000}{0.6c+330}$, where $t$ is the time in seconds and $c$ is the air temperature in Celsius. Sketch the graph of $t$ for $-20\le t\le 40$ where $t$ is the temperature in ${}^{\circ }\mathrm{C}$. Draw the line $t=3$ to find the temperature of the surrounding air when you hear the sound of thunder $3$ seconds after the flash of lighting from one kilometre away.

When lightning strikes, you see the flash almost instantly, but the sound of the thunder reaches you later, as sound travels at approximately $330 \mathrm{m}{ \mathrm{s}}^{-1}$. The speed of the sound is affected by temperature of the surrounding air. The time sound takes to travel one kilometre is modelled by $t=\frac{1000}{0.6c+330}$, where $t$ is the time in seconds and $c$ is the air temperature in Celsius. What is the air temperature when you hear the sound after $6$ seconds?

When you join a fitness centre for a trial, you get the first five sessions for free. After the first five sessions, the cost to join is $200$ euros. The average cost $c$ per session $\left(s\right)$ is modelled by $c=\frac{200}{(s-5)}$. Sketch the function and identify the horizontal and vertical asymptotes.

When you join a fitness centre for a trial, you get the first five sessions for free. After the first five sessions, the cost to join is $200$ euros. The average cost $c$ per session $\left(s\right)$ is modelled by $c=\frac{200}{(s-5)}$. Draw a line on the graph of $c=\frac{200}{(s-5)}$  to find when the cost per session averages $20$ euros.

On the same set of axes sketch $y=x+3$ and $y=\frac{1}{x+3}$ and on another set of axes sketch $y=x-2\text{ and }y=\frac{1}{x-2}$.